The first BipNonnormalVal4 can be obtained by inspecting the list [1]} of connected, non-normal, circulant graphs of valency 4:
\(K_5\) , \(C_m \wr \overline{K_2}\)  (with \(m\ge 3\) ) and \(K_2 \wr \overline{K_5}-5K_2\) .
For the reader's convenience, we reproduce the relevant parts of the proof in [1]}.
